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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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Given concentric circles with center O , Δ A B C is inscribed in the larger circle, as shown. If B C ¯ is tangent to the smaller circle at point T and A B = 8 , find the length of the radius of the smaller circle.

Chapter 6.2, Problem 48E, Given concentric circles with center O, ABC is inscribed in the larger circle, as shown. If BC is

To determine

To find:

The length of the radius of the smaller circle.

Explanation

Calculation:

Given, concentric circles with center O.

ΔABC is inscribed in the larger circle as shown below.

It is also given that, BC¯ is tangent to the smaller circle at point T and AB=8.

Now draw a line joining O and T.

OT is the radius of smaller circle and OA is the radius of the bigger circle.

So, OTCT.

OTC=90°.

From the figure, ABBC.

So, ABC=90°

Therefore,

OTC=ABC

And again from the figure,

OCT=ACB

Hence, ΔOTCΔABC by AA similarity

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